Integrated Magneto-Optic Modulator/Compensator System, Methods of Making, and Methods of Using the Same

ABSTRACT

Described herein is an integrated Faraday modulator and Faraday compensator (IFMC) system. Further described are methods of making an IFMC system, methods of customizing an IFMC system for a specific application, and methods of optimizing an IFMC system for a specific application. Further described is a robust 3D Finite Element Model (FEM) for designing and optimizing an IFMC system. Further described are optical instruments comprising an integrated Faraday modulator and Faraday compensator requiring only one optical crystal.

RELATED APPLICATIONS

This application claims the benefit of U.S. Ser. No. 14/169,280 filedJan. 31, 2014, now allowed, the entire disclosure of which is expresslyincorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with no government support. The government hasno rights in the invention.

BACKGROUND OF THE INVENTION

Diabetes is known to cause high levels of glucose to circulate in thebloodstream due to a lack of, or resistance to, the hormone known asinsulin. Several studies have shown that closely monitoring bloodglucose levels can significantly decrease the long-term health effectsof diabetes. Though conventional methods of personalized glucosemonitoring are done by extracting blood from the fingertip, morepatient-friendly methods of glucose monitoring are desired. One suchmethod involves the use of optical polarimetry.

A schematic illustration where a Faraday cell used in a device forsensing glucose in a birefringent medium is shown in PRIOR ART FIG. 1(which is a schematic illustration of one embodiment shown in theCameron et al. U.S. Pat. No. 7,245,952 issued Jul. 17, 2007). While suchdevices can provide ultra-sensitivity and control with the ability todiscern and control sub-millidegree rotations in the electric field oflight, such devices have several drawbacks. For instance, the Faradaycells are comprised of bulky custom-wound coils thereon. In use, theoverdriving can cause coil damage, and the coils are difficult toreplace. Additionally, such devices are difficult to tailor-design forcustom specifications. Moreover, modulator and compensator operation isprovided by two separate devices that each require an expensive opticalcrystal that has a desirable Verdet constant. In general, a lower Verdetconstant require a larger magnetic field. A material with a high Verdetconstant is one that has a relatively large amount of polarizationrotation under the application of a given magnetic field.

In the past, Faraday-based optical modulation and compensation wereperformed separately. These Faraday modulators and these Faradaycompensators each incorporated their own optical crystal—necessary inorder to produce the needed axial magnetic field component for a givenrotational depth by winding custom-fabricated inductive coils andplacing each crystal in the center of its own coil. Having a separateFaraday modulator and a Faraday compensator requires multiple opticalcrystals. Proper alignment of these separate optical crystals isproblematic and challenging since any light beam diverges after goingthrough the first crystal. The use of multiple optical crystals alsorequires matching (e.g., optically compatible) optical crystals in orderto achieve optical performance. Thus, even crystals purchased from thesame vendor often have slight variations unless they came from the samefabrication batch. These variations, in turn, cause a stressbirefringence in the light beam passing through the crystals.Furthermore, it is time-consuming and expensive to obtain sufficientlymatched optical crystals.

One previous attempt, described in Gobeli U.S. Pat. No. 6,246,893, tocombine both Faraday modulation and Faraday compensation with a singlecrystal mixed the two electric signals, and then applied the combinedelectric signal to a single inductive coil. One problem with thisapproach is that mixing the different types of electrical signals (i.e.,AC & DC) can be problematic on the high gain AC amplifier side, as theseamplifiers often have an inherent DC offset, or drift, which tends toconfound or mask the considerably smaller DC compensation drive termneeded to achieve optimal performance. As a result, such devicesutilizing such an approach cannot be implemented for accurate sensing ofcertain analytes having a small optical rotation, such as glucose.

To date, there are still many obstacles to the development of acommercially viable and manufacturable product suitable for opticalpolarimetric glucose detection. Thus, there is a need in the art forimproved and more cost-efficient systems for polarimetric and otheroptical sensing applications.

SUMMARY OF THE INVENTION

Provided herein is an integrated Faraday modulator and compensatorsystem having an AC magnetic field source in a first position inproximity to the optical material, where the AC magnetic field source isconfigured to generate a first magnetic field; and a DC magnetic fieldsource in a second position in proximity to an optical material, wherethe DC magnetic field source is configured to generate a second magneticfield. The first position and the second position are configured tocause the first magnetic field and the second magnetic field to besuperimposed on the optical material.

In certain embodiments, the optical material comprises a single opticalcrystal. In certain embodiments, superposition of the first and secondmagnetic fields within the optical material causes rotational modulationand compensation of a light beam passing through the optical material.In certain embodiments, the optical material is aligned on a first axis,the at least one AC magnetic field source is aligned on a second axis,the at least one DC magnetic field source is aligned on a third axis,where the first, second, and third axes are in a parallel andspaced-apart alignment.

In certain embodiments, one or more spaces are defined between theoptical material and the AC magnetic field source or the DC magneticfield source. In certain embodiments, orientation of at least one of thefirst magnetic field and the second magnetic field is adjustable withrespect to the each other and to the optical material. In certainembodiments, each of the AC and DC magnetic field sources is comprisedof an inductive coil circumferentially surrounding a ferromagnetic core,and the magnitude of the first magnetic field and the second magneticfield is dependent on the distance from each AC magnetic field sourceand DC magnetic field source as well as the magnitude of a currentdriving each inductive coil, while the direction of each magnetic fieldis perpendicular to a plane formed by the intersection of the currentand separation vectors using Equation 4:

${{B(r)} = {\frac{\mu_{0}}{4\pi}{\oint{\frac{I \times R}{R^{3}}{r_{0}}}}}};$

where bolded terms represent vector quantities, B(r) is the magneticfield at any point in space a distance r from the origin, go is thepermeability of free space (4π×10⁻⁷ N/A²), I is the current, R is thevector directed from the source point to r, and dr₀ is an element oflength along the current path.

In certain embodiments, the first magnetic field is generated by an ACcurrent from a first power source, and the second magnetic field isgenerated by a DC current from a second power source. In certainembodiments, each of the AC and DC magnetic field sources is comprisedof an inductive coil circumferentially surrounding a ferromagnetic core,where each the ferromagnetic cores defines an axis that is parallel to,and annularly spaced at about 90° intervals around, an axis defined bythe optical material.

In certain embodiments, the integrated Faraday modulator and compensator(IFMC) system has a modulation depth of about 1° and a maximumcompensation depth of about 0.0632°. In certain embodiments, the ACmagnetic field source comprises a high-powered resonant circuit havingone or more inductive coils and a magnetic core. In certain embodiments,the AC magnetic field source comprises a ferromagnetic core and anelectrically driven coil. In certain embodiments, different size, shape,and/or inductances of the coil provides a desire operational range ofrotations based on the maximum voltage supplied to the AC magnetic fieldsource.

In certain embodiments, the AC magnetic field source comprises avibrationally mounted permanent magnet. In certain embodiments, the ACmagnetic field source comprises at least one 100 mH inductor. In certainembodiments, the AC magnetic field source is comprised of a low-poweredresonant circuit having one or more inductive coils and a magnetic core.In certain embodiments, the DC magnetic field source comprises aferromagnetic core and an electrically driven coil. In certainembodiments, different size, shape, and/or inductances of the coilprovides a desire operational range of rotations based on the maximumvoltage supplied to the DC magnetic field source.

In certain embodiments, two or more AC magnetic field sources areconnected in series such that current flows in the same direction aroundeach coil, producing a collectively maximized axial component of themagnetic field along the optical material, and achieving an effectiveFaraday modulation to light passing through the optical material.

In certain embodiments, the optical material comprises a terbium-dopedglass (TDG) material; a terbium gallium garnet (TGG) material; or, anyttrium iron garnet (YIG) material. In certain embodiments, the opticalmaterial has a length-to-diameter aspect ratio of about 2.5. In certainembodiments, the optical material has a length of about 13.5 mm and adiameter of about 5.4 mm.

Further provided herein is a method of conducting integrated Faradaymodulation and Faraday compensation, the method comprising generating afirst magnetic field from an AC current, generating a second magneticfield from a DC current, and superimposing the first magnetic field andthe second magnetic field onto a single optical material.

Further provided herein is a method of measuring changes in a state ofpolarization of a beam of light, the method comprising generating afirst magnetic field from an AC current, generating a second magneticfield from a DC current, and superimposing the first magnetic field andthe second magnetic field onto a single optical material.

Further provided herein is a method of measuring changes in a state ofpolarization in a sample, the method comprising (a) passing polarizedlight through a sample or reflected from a surface of the sample suchthat the state of polarization of the light is changed; (b) allowing thechanged polarized light of step a) to pass through an optical materialhaving a desired Verdet constant; (c) providing separate AC and DCmagnetic field sources to the optical material; the AC magnetic sourceproducing a first magnetic field for fast polarization modulation; and,the DC magnetic source producing a second magnetic field forpolarization feedback compensation; (d) superimposing the separate firstand second magnetic fields within the optical material as the polarizedlight of step b) passes through the optical material of step c); (e)passing the polarized light of step d) through an analyzer; (f) allowingthe light of step e) to impinge onto a detector; (g) providing afeedback signal to at least one DC magnetic field source; (h) measuringchanges in a state of polarization in the sample; and, optionally (i)adjusting at least one DC magnetic field source based on the feedbacksignal of step g).

In certain embodiments, changes in the state of polarization arecalibrated, based on the feedback signal of step g), to one or more of:concentration of an analyte in the sample, layer thickness of thesample, surface characteristics of the sample, and material comprisingthe analyte and/or sample. In certain embodiments, step h) includesvarying ranges of modulation depths and/or varying ranges ofcompensation depths of one or more of the magnetic fields. In certainembodiments, the method further includes step j) controlling modulationand compensation depth by varying one or more of parameters selectedfrom: coil permeability, conductivity, wire radius, or number of turns,in the AC and/or DC magnetic field sources; location of the AC and/or DCmagnetic field sources with respect to each other and/or to the opticalmaterial; orientation of the AC and/or DC magnetic field sources withrespect to each other and/or to the optical material; and, current drivewithin the AC and/or DC magnetic field sources.

In certain embodiments, the sample is an optically active material. Incertain embodiments, the optically active material comprises glucose. Incertain embodiments, the glucose is present in aqueous humor of an eye,and the method comprises detection of glucose concentrations through theaqueous humor of the eye.

In certain embodiments, the sample comprises a material having surfacevariations. In certain embodiments, the material having surfacevariations comprises a thin film material.

In certain embodiments, a component apparatus is adjustable to allow foran operational range for modulation between 0° and 2°. In certainembodiments, a component apparatus is adjustable to allow for anoperational range for compensation between 0° and 0.5° withsub-millidegree rotational sensitivity. In certain embodiments, themethod comprises achieving a modulation depth of about 1° and a maximumcompensation depth of about 0.0632°.

In certain embodiments, an AC power supply to the AC magnetic fieldsource sustains a desired modulation depth to the magnetic fields beingsupplied to the optical material, and a DC power supply to the DCmagnetic field source supplies a sub-millidegree rotational sensitivityto the magnetic fields being supplied to the optical material.

Further provided herein is an integrated Faraday modulator andcompensator (IFMC) component apparatus comprising: a modular housingdefining a plurality of cavities configured position, with respect toeach other: (i) an optical material; (ii) at least one AC magnetic fieldsource disposed in a first position in proximity to the opticalmaterial, the AC magnetic field source being configured to generate afirst magnetic field; and, (iii) at least one DC magnetic field sourcedisposed in a second position in proximity to the optical material, theDC magnetic field source being configured to generate a second magneticfield; the apparatus further comprising a first power source disposedoutside the modular housing and configured to supply an AC current tothe AC magnetic field source, and a second power source disposed outsidethe modular housing and configured to supply a DC current to the DCmagnetic field source.

In certain embodiments, the apparatus further includes a polarizerdisposed outside the modular housing and configured to supply polarizedlight through the optical material. In certain embodiments, theapparatus further includes an analyzer disposed outside the modularhousing and configured to receive modulated and compensate light fromthe IFMC system. In certain embodiments, the apparatus further includesa detector disposed outside the modular housing and configured toreceive modulated and compensate light from the analyzer. In certainembodiments, the apparatus further includes a feedback signaling systemdisposed outside the modular housing and configured to receive modulatedand compensate light from the detector and configured to provide afeedback signal to at least one DC magnetic field source.

Various objects and advantages of this invention will become apparent tothose skilled in the art from the following detailed description of thepreferred embodiment, when read in light of the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWING

The patent or application file may contain one or more drawings executedin color and/or one or more photographs. Copies of this patent or patentapplication publication with color drawing(s) and/or photograph(s) willbe provided by the U.S. Patent and Trademark Office upon request andpayment of the necessary fees.

PRIOR ART FIG. 1: Schematic illustration of a glucose sensingpolarimeter utilizing a separate Faraday modulator and a separateFaraday compensator.

FIG. 2A: Exploded perspective schematic illustration of one embodimentof an integrated Faraday modulator/compensator (IFMC) system.

FIG. 2B: Schematic illustration of β=VBD, where a magnetic fieldcorrelates to Faraday rotation via Verdet constant.

FIG. 3: Exploded perspective schematic illustration of an IFMC systemintegrated in to a device for measuring of measuring changes in a stateof polarization in a sample.

FIGS. 4A-4B: Three-dimensional color map plot of magnetic field (G) ofan IFMC system in compensation (FIG. 4A), and modulation (FIG. 4B) aftera finite element model (FEM) analysis. The green curved lines representthe direction of current and the red arrows represent the fielddirection.

FIG. 5A: Schematic illustration of a single loop of current as appliedto the Biot-Savart Law.

FIG. 5B: Schematic illustration of a single loop geometry as shown withtwo-dimensional axial symmetry around the r-axis where the grey regionrepresents the boundary region (200 mm radius half-circle). The variouspoints represent analysis points while the wire cross-section is 5 mmfrom the origin.

FIGS. 6A-6B: Color map magnitude plot given in Gauss (FIG. 6A), andstreamline direction plot (FIG. 6B) of the magnetic field from a FEManalysis of a single loop of current.

FIGS. 7A-7B: Color map magnitude plot given in Gauss (FIG. 7A), andstreamline direction plot (FIG. 7B) of the magnetic field from a FEManalysis of three loops of current.

FIGS. 8A-8B: Graph (FIG. 8A) and table (FIG. 8B) displaying the errorbetween measured and FEM values of inductance and impedance for each ofsix coiled devices.

FIGS. 9A-9B: Three-dimensional color map plot of magnetic field (G) froma 470 mH inductor (FIG. 9A), and a two-dimensional plot of the axialcomponent of the magnetic field through a terbium-doped glass (TDG) rodfrom each inductor (FIG. 9B) after stationary FEM analysis. The greencurved lines in FIG. 9A represent the direction of current, and the redarrows represent the field direction.

FIGS. 10A-10B: Three-dimensional color map plot of magnetic field (G)from a 470 mH inductor (FIG. 10A), and a two-dimensional plot of theaverage axial component of the magnetic field through the TDG rod withrespect to the phase angle of the driving source from each inductor(FIG. 10B) after frequency domain FEM analysis. The green curved linesin FIG. 10A represent the direction of current, and the red arrowsrepresent the field direction.

FIG. 11A: A series of graphs showing FEM parametric voltage sweepresults from each coil in compensation. Starting with the upper leftplot and proceeding from left to right, top to bottom: 6.8 mH coil, 15mH coil, 68 mH coil, 100 mH coil, 220 mH coil, and 470 mH coil.

FIG. 11B: A series of graphs showing FEM parametric voltage sweepresults from each coil—in modulation. Starting with the upper left plotand proceeding from left to right, top to bottom: 6.8 mH, 15 mH coil, 68mH coil, 100 mH coil, 220 mH coil, and 470 mH coil.

FIGS. 12A-12B: Graphs showing the relationship between compensationdepth and driving voltage (FIG. 12A), and modulation depth and drivingvoltage (FIG. 12B), for each inductor based on FEM results.

FIGS. 13A-13B: Graphs showing FEM results comparing each coil—incompensation while being driven with a 1 VDC source (FIG. 13A), and inmodulation while being driven with a 10 V_(pk) source (FIG. 13B).

FIG. 14: Schematic illustration of an IFMC system used to measureFaraday rotations (both modulation and compensation). The thick linesrepresent the path of light whereas the thin lines represent electricalcommunication.

FIG. 15: Schematic illustration of a polarimetric glucose sensing systemusing an IFMC system. The thick lines represent the path of light, andthe thin lines represent electrical communication.

FIG. 16: Graphs showing prediction error in compensation (left) andmodulation (right) between FEM analysis and the physical measuredvalues.

FIG. 17: Graphs showing maximum compensation depth versus drivingvoltage (left), and maximum modulation depth versus average powerconsumption (right), for different inductors based on the FEM output.The horizontal blue line on the left plot indicates the minimumrotational requirement necessary for successful physiological glucosemeasurements. The minimum rotational requirement for a physiologicalglucose sensor is presented as the blue horizontal line on the plot onthe left. Points on the upper-left side of the plot on the rightrepresent the highest rotation-to-power ratio (RTPR).

FIGS. 18A-18B: Three-dimensional color map plot of magnetic field (G) ofthe IFMC system in compensation (FIG. 18A) and modulation (FIG. 18B)after FEM analysis. The green curved lines represent the direction ofcurrent, and the red arrows represent the field direction.

FIGS. 19A-19D: Graphs showing calibration and validation of hypoglycemicand hyperglycemic glucose detection. FIG. 19A is a calibration graph ofhypoglycemic glucose detection. FIG. 19B is a calibration graph ofhyperglycemic glucose detection. FIG. 19C is a validation graph ofhypoglycemic glucose detection. FIG. 19D is a validation graph ofhyperglycemic glucose detection.

FIG. 20: Schematic illustration of a programmable flow system. In theschematic, thick lines represent the fluid path while thin linescorrespond to electronic communication. The component labels are asfollows: flow cell (FC), photodetector (PD), pump 1 (P1), pump 2 (P2),pump 3 (P3), pump 4 (P4), central flask (CF), waste flask (WsF), waterflask (WaF), glucose flask (GIF), stir plate (SP), microcontroller (MC),and motor driver (MD). P3 is located behind P2, and P4 is located behindP1.

FIG. 21: Perspective view of a 1 cm flow cell capable of being mountedto a polarimeter for stable continuous measurements.

FIG. 22: Graph of glucose concentration (mg/dL) versus time (min),showing a 500-minute continuous polarimetric glucose detection test asmeasured with the IFMC system. The data is plotted against the actualphysiological glucose profile used during the test.

FIG. 23: Graph of glucose concentration (mg/dL) versus time (min) for afirst test, showing a 20-minute baseline-corrected, 60-secondmoving-averaged data profile of the data shown in FIG. 22. The data isplotted against the actual physiological glucose profile used during thetest.

FIG. 24: Graph of glucose concentration (mg/dL) versus time (min) for asecond test, showing a 500-minute continuous polarimetric glucosedetection test as measured with the IFMC system (left), and the20-minute baseline correct, 60-second moving averaged data profile(right). Both data sets are plotted against the actual physiologicalglucose profile used during the test.

FIG. 25: Graph of glucose concentration (mg/dL) versus time (min) for athird test, showing a 500-minute continuous polarimetric glucosedetection test as measured with the IFMC system (left), and the20-minute baseline corrected, 60-second moving averaged data profile(right). Both data sets are plotted against the actual physiologicalglucose profile used during the test.

FIG. 26: Graph of glucose concentration (mg/dL) versus time (min) for afourth test, showing a 500-minute continuous polarimetric glucosedetection test using a clinical diabetic profile as measured with theIFMC system (left), and a 20-minute baseline corrected, 60-second movingaveraged data profile (right). Both data sets are plotted against theactual physiological glucose profile used during the test.

FIG. 27: Graph of glucose concentration (mg/dL) versus time (min) for afifth test, showing a 500-minute continuous polarimetric glucosedetection test using a near-step change profile as measured with theIFMC system (left), and a 20-minute baseline corrected, 60-second movingaveraged data profile (right). Both data sets are plotted against theactual physiological glucose profile used during the test.

DETAILED DESCRIPTION OF THE INVENTION

Throughout this disclosure, various publications, patents and publishedpatent specifications are referenced by an identifying citation. Thedisclosures of these publications, patents and published patentspecifications are hereby incorporated by reference into the presentdisclosure in their entirety to more fully describe the state of the artto which this invention pertains.

General Description

Optical polarimetry is the measurement of the polarization state oftransverse electromagnetic waves (TEM). More specifically, a polarimeteris a device capable of measuring rotation in the state of linearpolarization when a transverse electromagnetic wave passes through anoptically active material, such as glucose. A material is opticallyactive if the electric field of a linear plane wave rotates around anaxis parallel to the direction of travel through the material. Thesetypes of materials are classified based on the direction of rotation inthe electric field. If a plane wave rotates in a clockwise (positive)direction when facing the source of light, the material isdextrorotatory (d-rotatory). If a wave rotates in a counterclockwise(negative) direction, it is levorotatory (l-rotatory). Optically activematerials possess a separate refractive index that affects right (n_(R))and left (n_(L)) circularly polarized light, a material property knownas circular birefringence. Given that the linear polarization is thesuperposition of two opposing circular components of equal magnitude,the components become out of phase when travelling through an opticallyactive material, resulting in a rotated plane wave. The amount ofrotation (a) can be quantified based on the indices of refraction,material path length (L), and vacuum wavelength (4), as shown inEquation 1:

$\begin{matrix}{\alpha = {\frac{180{^\circ}\; L}{\lambda_{0}}\left( {n_{L} - n_{R}} \right)}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

The concept of optical activity holds true for glucose and other chiralmolecules when dissolved in solution, based on their overallconcentration. Chiral molecules have multiple enantiomers, which areidentical compounds except in how they react with other chiral moleculesand in how they rotate linearly polarized light. Complex biologicalmolecules, such as glucose, typically occur in nature as one enantiomer,meaning that a net rotation in polarization can be observed in samplescontaining these compounds. The relationship between rotation, samplepath length, and concentration (C) is given as a temperature-(T),wavelength-(λ), and pH-dependent constant known as specific rotation,[α]_(λ,pH) ^(T), as shown in Equation 2:

$\begin{matrix}{\lbrack\alpha\rbrack_{\lambda,{pH}}^{T} = \frac{\alpha}{LC}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

Given the specific rotation of D-glucose (63.2°/(dm*g/mL) at 543.5 nm),a physiological change of 10 mg/dL in concentration results in arotational shift of 0.632 millidegrees in a linearly polarized beam oflight when passed through a 1 cm sample. Therefore, a noninvasivepolarimetric detection system for glucose detection should be able toachieve sub-millidegree measurement sensitivity.

Although signal modulation allows for significant noise rejection, thedetection source of a polarimeter should still be capable of measuringsub-millidegree rotations. Therefore, a null-point, closed-loop signalfeedback mechanism that can controllably compensate for signal rotationcaused by glucose can be utilized. When digitally controlled, thefeedback mechanism can detect glucose concentrations in real time. Inorder to control rotational modulation and compensation in a real-time,closed-loop system, a phenomenon known as Faraday rotation can beutilized. This method of rotation is similar to that which occurs in anoptically active medium. However, the oscillating electric fieldcomponent of the propagating light causes elastically bound electronswithin an optical material to vibrate in a circular orbit. Thegeneration of this current in combination with the axial component of anexternal magnetic field produces a force on the electrons. This force,along with the elastic restoring force of the electrons, creates twoseparate dipole moments, leading to two separate indices of refraction(n_(R) and n_(L)), and ultimately causing circular birefringence. Therelationship between rotation (a), path length (L), and the magneticfield strength in the direction of travel (B) is held by a temperature-and wavelength-dependent proportionality constant known as the Verdetconstant (V) as shown in Equation 3:

α=VBL  Equation 3

Materials which typically experience this phenomenon, such as terbiumgallium garnet (TGG) and terbium-doped glass (TDG), can be veryexpensive and difficult to produce such that stress- andtemperature-induced birefringence do not play a role in rotationalinterference.

Faraday rotation is most useful in polarimetry for its ability tocontrollably modulate and compensate polarized light. The precisecontrol required for sub-millidegree rotation sensitivity is achievedthrough voltage-driven inductive coils based on the relationship betweena moving charge and magnetic field as shown in the Biot-Savart Law:

$\begin{matrix}{{B(r)} = {\frac{\mu_{0}}{4\pi}{\oint{\frac{I \times R}{R^{3}}{r_{0}}}}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

Bolded terms in Equation 4 represent vector quantities, B(r) is themagnetic field at any point in space a distance r from the origin, no isthe permeability of free space (4π×10⁻⁷ N/A²), I is the current, R isthe vector directed from the source point to r, and dr₀ is an element oflength along the current path. As seen in Equation 4, the magnitude ofthe magnetic field is dependent on the distance from the source as wellas the magnitude of the driving current, while the direction of thefield is perpendicular to the plane formed by the intersection of thecurrent and the separation vectors.

It is to be understood that the concept of Faraday rotation is onlydependent on the field component that is parallel to the axis of travelof the light source and inductive coils are typically used to generatethis component. The representation of a single loop of current from aninductor as applied to the Biot-Savart Law can be seen in FIG. 5A. Basedon this geometry, it can be seen that r₀=r₀ cos(θ){circumflex over(x)}+r₀ sin(θ)ŷ+z₀{circumflex over (z)}, r=x{circumflex over(x)}+yŷ+z{circumflex over (z)}, R=r−r₀=[x−r₀ cos(θ)]{circumflex over(x)}+[y−r₀ sin(θ)]ŷ+[z−₀]{circumflex over (z)}, and dr₀=[−r₀sin(θ){circumflex over (x)}+r₀ cos(θ)ŷ]dθ since r₀ is constant aroundthe loop. By holding the current constant, as is the case in the Faradaycompensator, it can be moved outside of the integral and the crossproduct of dr₀ and R can be solved. The vector quantity Q wasarbitrarily assigned as the solution to this cross product as given by:

Q _(x) =[zr ₀ cos(θ)−z ₀ r ₀ cos(θ)]dθ{circumflex over (x)}  Equation 5

Q _(y) =[zr ₀ sin(θ)−z ₀ r ₀ sin(θ)]dθŷ  Equation 6

and,

Q _(z) =[r ₀ ² −yr ₀ sin(θ)−xr ₀ cos(θ)]dθ{circumflex over(z)}  Equation 7

By letting α=x²+y²+z²+z₀ ²+r₀ ²−2zz₀, the magnitude of the separationvector R can be calculated to be

R=√{square root over (α−2xr ₀ cos(θ)−2yr ₀ sin(θ))}  Equation 8

Finally, Equations 5 through 8 can be substituted into Equation 4 andthe component representation of the magnetic field from a single,uniform loop of current at any point in space can be given as

$\begin{matrix}{{B_{x}\left( {x,y,z} \right)} = {\frac{\mu_{0}I}{4\pi}{\oint_{0}^{2\pi}{\frac{\left\lbrack {{{zr}_{0}{\cos (\theta)}} - {z_{0}r_{0}{\cos (\theta)}}} \right\rbrack}{\begin{bmatrix}{\alpha - {2{xr}_{0}\cos (\theta)} -} \\{2\; {yr}_{0}{\sin (\theta)}}\end{bmatrix}^{3/2}}{\theta}}}}} & {{Equation}\mspace{14mu} 9} \\{{{B_{y}\left( {x,y,z} \right)} = {\frac{\mu_{0}I}{4\pi}{\oint_{0}^{2\pi}{\frac{\left\lbrack {{{zr}_{0}{\sin (\theta)}} - {z_{0}r_{0}{\sin (\theta)}}} \right\rbrack}{\begin{bmatrix}{\alpha - {2{xr}_{0}\cos (\theta)} -} \\{2\; {yr}_{0}{\sin (\theta)}}\end{bmatrix}^{3/2}}{\theta}}}}}{{and},}} & {{Equation}\mspace{14mu} 10} \\{{B_{z}\left( {x,y,z} \right)} = {\frac{\mu_{0}I}{4\pi}{\oint_{0}^{2\pi}{\frac{\begin{bmatrix}{r_{0}^{2} - {{yr}_{0}\sin (\theta)} -} \\{{xr}_{0}{\cos (\theta)}}\end{bmatrix}}{\begin{bmatrix}{\alpha - {2{xr}_{0}\cos (\theta)} -} \\{2\; {yr}_{0}{\sin (\theta)}}\end{bmatrix}^{3/2}}{\theta}}}}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

Based on Equations 9, 10, and 11, it can be seen that solving for themagnetic field at a single point in space due to a loop of current willrequire complex numerical integration. Given that a coil inductor can beviewed as a series of current loops when in steady state, superpositioncan be used to evaluate the total field strength at various points inspace. However, these calculations get progressively more complex whendifferent materials, shapes, and orientations are evaluated withmultiple inductors at several points in space. Also, the model no longerholds true in an AC driven coil, such as that required for Faradaymodulation. As such, described further herein is a finite element model(FEM) which is a computational method capable of solving thousands ofordinary differential equations (ODEs), partial differential equations(PDEs), and integral equations simultaneously over complicated domainsby solving a matrix of nodes applied with initial conditions based onthe materials and physics used. The FEM was designed for accurate andefficient field calculations in both compensator and modulator coils.

In use, a Faraday modulator modulates the electric field vector byimposing a certain frequency. Such modulation, in turn, creates a largeAC signal. In use, a Faraday compensator negates (e.g., compensates for)the optical rotation of the optically active sensor. Such compensation,in turn, creates a small DC signal.

The operation of a Faraday-based, closed-loop, null-point feedbackpolarimeter can be modeled mathematically using Jones vectors andmatrices which are used to represent the electric field of polarizedlight and how it interacts with various optical components. A Jonesvector is a component representation of the electric field of apolarized wave. Different optical components are represented as Jonesmatrices which describe the behavior of polarized light through aspecific component. By multiplying the vector representation of thepolarized electric field by various Jones matrices, the behavior of anoptical system such as a polarimeter can be predicted. This technique isespecially useful to represent the light intensity that is measured by aphotodetector in Faraday-based optical polarimetry. The Jones model usedto represent the detected signal intensity in such a system is shown inEquation 12:

$\begin{matrix}{E^{2} = {\left( {\varphi^{2} - \frac{\theta_{m}^{2}}{2}} \right) + {2{\varphi\theta}_{m}{\sin \left( {\omega_{m}t} \right)}} - {\frac{\theta_{m}^{2}}{2}{\cos \left( {2\omega_{m}t} \right)}}}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

where φ is the difference in rotation between the optically activesample and that of the Faraday compensator, θ_(m) is the modulationdepth, ω_(m) is the modulation frequency, and t is time. The model hasthree components: a DC offset, a modulated component, and a 2ω_(f)component. The 2ω_(f) component is present because photodetectors areonly sensitive to light intensity, which is always a positive value.Therefore, when the rotational modulation is centered on the null planeof the analyzer, it appears as though the detected signal has afrequency that is twice the driving frequency due to rotationalsymmetry. However, when an optically active sample is introduced, therotational modulation is no longer centered on the null plane, so asingle frequency component exists as well. When this occurs, the lock-inamplifier detects the single frequency component and produces an outputbased on the non-orthogonal relationship to the reference sine wave. Theprinciple of the null-point feedback system is to continuously apply aDC voltage to the compensator coil that is proportional to the magneticfield and, in turn, the amount of rotation caused by the opticallyactive sample in order to force φ to zero. This is done by continuouslymeasuring the lock-in output and compensating for rotations inpolarization by a digital proportional-integral-derivative (PID)controller. When the signal is completely nulled, only the 2ω_(f)component is present, the lock-in output is zero, and the PID outputcorresponds to the concentration of glucose within a fixed-lengthsample. The compensator voltage can then be correlated to the glucoseconcentration through least-squares linear regression, and the model canbe used to predict unknown concentrations.

Electro-optic modulators and compensators (EOMs) are optical devicescapable of imposing or affecting the phase, frequency, amplitude, orpolarization of light. Various forms of EOMs exist, and they are notlimited to Faraday cells. Some other exemplary types of EOMs includeliquid crystals, Pockets cells, Kerr cells, and photoelastic modulators.

In a Faraday cell, the core of the device is an optical rod doped withparamagnetic ions. The Faraday rotation of the electric field (β) isproportional to the product of the Verdet (V) constant of the opticalcrystal and the magnetic field (B) across the length (d) of the crystal,as illustrated in Equation 3:

β=VBd  Equation 3

Integrated Faraday Modulator/Compensator (IFMC) System

Described herein is an integrated Faraday modulator/compensator (IFMC)system that keeps electric signals separate, and then combine thesignals in the magnetic field. In such embodiments, two magnetic fieldsare produced from two separate electric signals, and are then combinedon the optical material; when the magnetic fields of the two electricsignals are in the same time and space, they superimpose on top of eachother. This eliminates the problem of DC drift from mixing electricsignals, and eliminates the need for a second optical crystal, whilestill maintaining desired performance characteristics.

The IFMC system provides control of Faraday rotation through themagnetic field, which is generated from current travelling around aninductive coil. FIG. 2A shows an exploded perspective schematicillustration of one embodiment of an integrated Faradaymodulator/compensator (IFMC) system 10, while FIG. 2B provides aschematic illustration of β=VBD, where a magnetic field correlates toFaraday rotation via the Verdet constant.

In the embodiment shown in FIG. 2A, the IFMC system 10 includes anoptical component 12, at least one compensator 14 (e.g., source of a DCmagnetic field 14), and at least one modulator 16 (e.g., source of an ACmagnetic field 16). The compensator 14 illustrated in FIG. 2 includescoils 24 wound around a ferromagnetic core 34. In the embodiment shownin FIG. 2, a plurality of modulator components 16 a, 16 b, 16 c areshown. Each modulator 16 illustrated in FIG. 2 includes coils 26 a, 26b, 26 c, respectively, wound around ferromagnetic cores 36 a, 36 b, 36c, respectively.

It is to be understood that, while one geometrical configuration of theIFMC system 10 is shown in FIG. 2A, many other configurations arepossible. For example, in certain embodiments, the IFMC system 10 canhave more than one compensator component 14 and/or one or more modulatorcomponents 16.

Certain embodiments of the IFMC system include gaps 56 between thecompensator component 14 and the optical crystal, and/or between themodulator components 16 and the optical crystal 12. The gaps 56 allowfor air flow channels to be created, reducing the amount of heating onthe crystal 12. Furthermore, in certain embodiments, the IFMC system 10requires less power since there can be fewer windings in the compensatorcoil 24 and/or the modulator coils 26 than in previous devices, thusfurther reducing the heating on the crystal 12.

In general, the IFMC system has two or more inductive coils that areplaced within close proximity to the optical material, one formodulation and one for compensation. The location and orientation of theinductive coils with respect to the optical material within the housingor component apparatus can be controlled by fixture inserts and spacers.Coil type selection, location, orientation, and drive characteristicsare variables that can be used to control modulation and compensationdepth, so as to customize the IFMC system for specific applications.Mathematical or computational models can be used for predictingrotational characteristics based on component apparatus parameters.

In certain embodiments, the DC magnetic field source 14 is composed of aseparate inductive coil for highly sensitive rotational control.Rotational modulation and compensation occurs within the opticalcomponent by the superposition of separate magnetic fields within theoptical material. In certain embodiments, the AC magnetic field source16 is composed of a high-powered resonant circuit having of one or moreinductive components within close proximity to the optical material 12,or a vibrationally mounted permanent magnet within close proximity tothe optical material 12.

The IFMC system 10 integrates the functionality of both polarizationmodulation and compensation in a single-crystal system while maintainingperformance standards. Separate Faraday components are not needed, and asingle optical material can be used for both modulation and compensationbased on the superposition of magnetic fields from separate inductivecomponents. In the embodiment shown, ferrite-core inductors can beplaced within proximity of the optical material in order to provide thenecessary field strength along a longitudinally extending axis of theoptical material. In certain embodiments, the IFMC system does notrequire specially designed custom inductive coils because it is capableof utilizing standard commercially-available inductive coils to achieverequired performance. In certain embodiments, the IFMC system has amodular design which can be easily adapted for specific applicationsrequiring different performance standards.

Referring now in particular to FIG. 3, one embodiment of the IFMC systemcan be included in a modular unit 42 having an outer housing 44 and aninner housing 46, where the outer housing 44 is fastened to a cage mount48 via one or more mounting bolts 8. The inner housing 46 has one ormore fixture slots 50 a, 50 b, 50 c, 50 d designed to house the opticalcrystal 12, modulator components 16 a, 16 b, 16 c, and compensatorcomponent 14. The optical crystal 12 is held in place with a clamp 30.The modulator components 16 a, 16 b, 16 c are composed of inductivecoils 26 a, 26 b, 26 c wrapped around ferromagnetic cores 36 a, 36 b, 36c, each contained within a body shell 22 a, 22 b, 22 c and a cap 32 a,32 b, 32 c. The compensator component 14 is composed of an inductivecoil 24 wrapped around a ferromagnetic core 34. The compensator 14 isheld in place with an insert rod 28 a, and each of the modulators 16 a,16 b, 16 c is held in place with an insert rod 28 b, 28 c, 28 d.

As shown in FIG. 3, the modular unit 42 utilizes multiple inductors: atleast one modulator coil 26 and a compensator coil 24. Each inductorcoil 24, 26 can be driven with a different signal. Each inductor coil24, 26 generates a respective magnetic field. The two magnetic fieldsare then combined. The inductive coils 24, 26 can be placed in parallelor in series; many designs are possible. The specific coils to use andthe exact design of the coils depends on the application; the geometryand design of the coils can be tailored specifically and optimized forthe desired application using a FEM as described herein. In certainembodiments, the ends of the coils are connected to separate powersupplies.

In certain embodiments, the optical crystal 12 is in a position wherethe compensator coil 24 and the modulator coils 26 a, 26 b, 26 c arearranged annularly around, and in close proximity to, the opticalcrystal 12, as shown in FIG. 3. However, in certain embodiments, theoptical crystal 12 need not be oriented in the center of the housing 4or the coils 14, 16, and the compensator 14 and/or modulators 16 neednot be in an annular arrangement. In certain embodiments, the opticalcrystal 12 is in a spaced-apart relationship to the compensator 14 andthe modulators 16 such that one or more gaps 56, or air flow channels,exist between the optical crystal 12 and the compensator 14 and themodulators 16, as seen in FIG. 2A.

In the embodiment shown in FIG. 3, the cage mount 48 has an opticalwindow 53 configured to allow electromagnetic radiation from a lightsource, such as a laser, to pass through the modular unit 42. Anassociated plug 52 for the electrical connections to the driveelectronics is inserted into the plug mount 18. The cage mount 48 andthe outer housing 44 can also have multiple connection ports 20 that areconfigured to physically integrate the modular unit 42 into apolarimetric or other optical sensing system (for example, see FIG. 20,discussed below). It is to be understood that many alternative designsfor a modular IFMC system 10 are possible, and are within thecontemplated scope of the disclosure herein.

The outer housing 44 for the IFMC system 10 can be formed to suit adesired end-use application. For example, in one embodiment, the housing44 can be manufactured through a three-dimensional printing process,using for example SolidWorks® structural models, or any other similartechniques. The ability to custom-tailor a housing 44 allows for customIFMC systems to be designed to meet particular specifications for agiven end-use application.

The optical crystal 12 in the IFMC system 10 can be a suitable opticalcrystal 12 that exhibits the Verdet property. Suitable optical crystals12 include, but are not limited to, terbium gallium garnet (TGG)crystals, terbium-doped glass (TDG) crystals, and yttrium iron garnetcrystals. In certain embodiments, the IFMC system 10 utilizes a singleTDG crystal having a generally rod-shape, and inductive coils that arecapable of replacing the custom designed components used in traditionalFaraday-based systems. Suitable inductive coils 24, 26 include, but arenot limited to, ferrite core inductors. The utilization of ferromagneticcores 34, 36 such as ferrite cores, can result in reduced powerconsumption compared to other designs. Combined, the use of a singleoptical crystal and ferrite core inductors significantly minimizes sizeand cost by eliminating the need for custom-designed coils and multipleoptical components.

The IFMC system 10 also overcomes the problem plaguing the art of coilheating, which can affect crystal properties by causing thermalinstability—where an inductive coil is wrapped around the crystal, suchthat when the coil heats up, the crystal is also heated.

Finite Element Model (FEM)

The single-crystal modular design of the IFMC system 10 can usedifferent types of ferromagnetic core inductors. In another aspect,there is provided herein a finite element model (FEM) system whichallows for further customization of the IFMC system 10.

For example, without a model, the inductor identification, placement,and interaction can be difficult to characterize in order to achieve arequired performance. This is generally because the addition ofnon-uniform shapes, various materials, and non-symmetric orientationsmake predictive calculations extremely complex. Thus, provided herein isa non-limiting example of optimization for specific designspecifications using a robust three-dimensional (3D)finite-element-model (FEM) system. The FEM uses magnetic fields, such asthose illustrated in FIGS. 4A-4B. The FEM can completely simulate aparticular design of an IFMC system 10, thus enabling the IFMC system tobe custom-designed for specific user specifications.

The FEM allows for off-the-shelf components to be optimized to achievecertain operational parameters. For example, a user could specify apredefined modulation depth and compensation range. The 3D model canthen be used to identify the required, commercially available inductivecomponents and the necessary layout to meet the required specifications.Any issues with the generation of the magnetic/electric field can beverified through the 3D visualization and can be addressed before theactual device is assembled.

Examples of Applications

The systems, devices and methods disclosed herein are useful forpolarimetric and other optical sensing applications, and involvemeasuring changes in the state of polarization of light by thesuperposition of magnetic fields for combined Faraday-based modulationand compensation. In certain embodiments, polarized light is passedthrough a sample or reflected from a surface such that the state ofpolarization changes. The light is then allowed to pass through acomponent containing an optical material, such as a terbium-containingcompound, which is within close proximity to separate AC and DC magneticfield sources. The AC magnetic field source produces a high-powered ACmagnetic field for fast polarization modulation, while the DC magneticfield source produces a lower-powered DC magnetic field for polarizationfeedback compensation. The separate magnetic fields are superimposed intime and space within the optical material through which the light alsopasses. The light then passes through an analyzer prior to impingingonto a detector. In certain embodiments, feedback from the systemutilizes a highly sensitive, lower-powered DC magnetic field source tonullify the polarization offset corresponding to the sample of interest.

The IFMC system can be used for detecting changes to the state ofpolarization in the light signal due to optically active materials orsurface variations. A non-limiting example of such an applicationinvolves the noninvasive detection of glucose concentrations through theaqueous humor of the eye. Changes in the state of polarization can becalibrated to concentration, layer thickness, surface characteristics,or material percentage based on the feedback signal. The separation ofAC and DC magnetic field sources allows for highly sensitive rotationalmeasurements, easy customization to specific applications, the use of asingle optical material component, and a wide range of modulation depthscapable of being combined with a wide range of compensation depths.

In certain embodiments, the design parameters of the IFMC system allowfor an operational range for compensation between 0° and 0.5° withsub-millidegree rotational sensitivity. The separation of the magneticfield sources allows for highly sensitive control of separate driveelectronics for modulation and compensation; that is, high-powered driveelectronics can sustain the required modulation depth while alow-powered DC supply can provide sub-millidegree rotational sensitivitywithout interference from mixed signals. The superposition of theseparate magnetic fields provides stabile modulation andhighly-sensitive compensation in a single optical component device forrotational measurements.

In certain embodiments, the IFMC system can achieve modulation depthsabove 1°, and when operating in a compensated closed-loopglucose-sensing polarimetry configuration, can achieve glucoseprediction errors of 1.8 mg/dL and 5.4 mg/dL under hypoglycemic andhyperglycemic conditions, respectively.

The IFMC system can be implemented into multispectral systems forfurther component consolidation in multi-analyte or birefringentconditions. Drift in such systems comprising an IFMC system may beminimized by rigidly coupling the optical components together andeliminating excess vibration in a compact, hand-held device. The IFMCsystem is particularly versatile when miniaturized so as to fit into ahand-held instrument. In certain embodiments, the IFMC system has nomoving parts, and therefore is free of mechanically produced noiseproblems.

In certain embodiments, the IFMC system and methods described hereinprovide optimized application-specific performance using lower-costfabrication components with a modular design approach. Sub-millidegreecontrol for linear polarization applications is possible with an IFMCsystem.

Though various examples pertaining to glucose sensing are describedherein, it is to be understood that the IFMC system is not limited touse in glucose-monitoring applications. Rather, the IFMC system is alsosuitable for use in a wide variety of applications and instruments,including any type of device that incorporates modulators. By way ofnon-limiting examples, the IFMC system is also useful in devices,instruments, or systems for Fourier transform infrared (FTIR)spectroscopy, optical coherence tomography, and optically-active Ramanspectroscopy.

The IFMC system can also be utilized in devices for sensing anyoptically active analyte including, but not limited to, glucose, lacticacid, albumins, and proteins. The IFMC system is particularly useful forthin-film ellipsometry and in vivo and multi-analyte noninvasivesensing.

Examples of FEM

Optimization for specific design specifications can be provided throughFEM. Use of such FEM allows for the IFMC system to be tailor-designedfor custom applications, or to minimize power consumption Minimizingpower consumption, while still maintaining operational specifications,is especially important for hand-held devices so that they can bepowered through rechargeable battery subsystems.

Another benefit of using a FEM is that various spatially dependentvariables can be solved within a complex geometry with varying materialproperties through discrete methods. Through the FEM, the volume orsurface of interest is divided into an array of discrete elements offinite size and shape. Each element is assigned a specific set ofmaterial properties based on the physics that are being solved, such aselectrical conductivity, magnetic permeability, and electricalpermittivity in the case of electromagnetic fields. The array ofelements together is known as the mesh, which is used to collectivelydefine the overall system.

The size of individual elements throughout the mesh may vary dependingon the intricacies of the model in order for the analysis to converge toa representative result. The intersections of elements create analysispoints, or nodes, which provide points in space that can numericallyrepresent a solution. Various systems of equations can then be assignedto the model, which are solved using discrete numerical andcomputational methods based on a set of initial boundary conditionsapplied to the model and the interactions between individual elements.Such models allow for multiple ordinary and partial differential, aswell as integral, equations to be solved simultaneously, depending onthe approximations within each finite element. The results can becompiled as a fully integrated model in order to represent collectiveinteractions at various regions of interest. The mathematical theoryinvolved is based on the Galerkin method, which can be used to convertcontinuous problems into discrete approximations.

There are several software applications suitable for solving FEMs with aheavy focus on structural mechanics. COMSOL® Multiphysics is one suchpackage, which can solve models implementing several complementaryphysics such as structural mechanics, thermodynamics, fluid flow,chemical reactions, and electromagnetism based on independent ordependent interactions. The AC/DC Module within COMSOL® allows for theanalysis of magnetic field physics in three-dimensional structures. Themagnetic fields interface within this module solves Ampere's Law for themagnetic vector potential based on the following equations:

J _(e)=(jωσ−ω ²ε₀ε_(r))A+∇×*(μ₀ ⁻¹μ_(r) ⁻¹ B)−σν×B  Equation 14

B=∇×A  Equation 15

where J_(e) is the external current density, j is the imaginary unit, ωis frequency, σ is conductivity, ε₀ is the vacuum permittivity, ε_(r) isthe relative permittivity, A is the vector potential, ∇ is the deloperator, μ₀ to is the vacuum permeability, μ_(r) is the relativepermeability, B is the magnetic field vector, and ν is the currentvelocity vector of the conductor. These equations can be solved in bothstatic and frequency-dependent conditions, providing an ideal system forpredicting Faraday rotations in compensation as well asfrequency-dependent modulation.

Also provided herein is a method of using such results to optimize aFaraday-based optical polarimeter for a variety of applications. Giventhat a coil inductor can be viewed as a series of current loops when insteady state, superposition can be used to evaluate the total fieldstrength at various points in space in a multi-turn coil. However, thesecalculations get progressively more complex when different materials,shapes, and orientations are evaluated with multiple inductors atseveral points in space. Thus, described herein is a method of using aFEM to design an integrated modulation and compensation device thateliminates the need for multiple optical crystals. In certainembodiments, the FEM is used to optimized the integrated modulation andcompensation device for noninvasive glucose-monitoring applications. Asdescribed in the examples herein, a 3D FEM was developed in order topredict the magnetic fields caused by various inductive coils in orderto custom-design an IFMC system for noninvasive glucose sensingapplications.

EXAMPLES Example 1 Building a FEM and Testing an IFMC System

A FEM was designed for accurate and efficient field calculations in bothcompensator and modulator coils, such that magnetic fields caused by theinductive currents could be determined for a wide range of off-the-shelfinductors. The results were used to select specific coils to beimplemented in a modular IFMC system based on the requirements of anoninvasive physiological glucose sensor of 1° modulation depth and0.0632° for maximum compensation depth.

The FEM was designed using the AC/DC Module in COMSOL® Multiphysics(COMSOL, Inc., Burlington, Mass.). To begin, a model was created basedon the geometry of FIG. 5A, which represents a single loop of currentusing the 2D axisymmetric dimension scheme, the magnetic fields physicsselection, and the stationary solver sequence. A single loop of currentwith a radius of 5 mm and a magnitude of 71 mA was evaluated using theBiot-Savart Law in a stationary analysis. A cross section of the loop ofwire was drawn 5 mm away from the rotational axis and was assigned as asingle-turn coil domain with an initial vector potential of zero, theconductivity of copper, and an applied current of 0.0701 A. Then, thematerial properties of air were defined within the boundary region (200mm radius half-circle) and a free triangular mesh was applied to breakthe model into finite elements before launching the solver. With theloop centered at the origin around the z-axis, the selected analysispoints were (0, 10, 0), (0, 10, 10), and (0, 0, 0), given in mm in they-z plane and referenced as pt1, pt2, and pt3, respectively (as shown inFIG. 5B). The FEM resulted in a magnetic field at these points ofmagnitude 7.57 mG, 3.02 mG, and 88.11 mG, respectively. After solvingthe FEM, equations representing the magnetic field from a single,uniform loop of current at any point in space were solved in Mathcad(PTC, Needham, Mass.) with the same initial conditions at various pointsin space in order to compare the FEM with the mathematical model.

FIG. 5B displays an image of the single loop geometry shown with 2Daxial symmetry around the r-axis. The process was then repeated for athree-loop coil domain in COMSOL® and using superposition of theBiot-Savart model for three different loops. Table 1 displays thecalculated error between the FEM and the Biot-Savart Law.

TABLE 1 Initial 2D FEM-predicted magnetic field results as compared tothe Biot-Savart Law calculations Single Loop Analysis Triple LoopAnalysis Biot- Biot- Coordinate FEM Savart Error FEM Savart Error Point(mm) (mG) (mG) (%) (mG) (mG) (%) (0, 10, 0) 7.57 7.60 0.39 22.75 22.760.04 (0, 10, 10) 3.02 3.03 0.33 9.04 9.10 0.66 (0, 0, 0) 88.11 88.090.02 264.13 264.03 0.04

The FEM results are also shown in FIGS. 6A-6B, which show aconcentration of field strength in close proximity to the coil (FIG. 6A)with field lines extending perpendicularly to the current direction(FIG. 6B). However, the field lines appear distorted around the boundarylayer, indicating the need for an infinite element domain surroundingthis boundary in order to resolve proper directionality. Furthermore,the total current-induced magnetic field at any point in space is thevector sum of all the individual contributions. Therefore, a simple sumof three identical current loops was also investigated. The FEM resultedin a magnetic field at pt1, pt2, and pt3 of magnitude 22.75 mG, 9.04 mG,and 264.3 mG, respectively. The Biot-Savart Law resulted in magnitudesof 22.76 mG, 9.10 mG, and 264.03 mG, respectively. Based on theseresults, the average error between the FEM and Biot-Savart Law wascalculated to be 0.25%. These results are shown in FIGS. 7A-7B. Theseresults demonstrate that there is a good correlation between the FEMprediction and the actual calculated value for inductive magneticfields, establishing that the model can be used for more elaborate 3Dcoil configurations with the addition of an infinite element domain.

After the 2D axisymmetric FEM was related to the Biot-Savart Lawcalculations for a single loop and three loops of current, more complex3D models were built and tested in COMSOL® to evaluate the magneticfield produced by different coils for use in Faraday compensation andmodulation. In order to evaluate the models against physical rotationalmeasurements, six ferrite core inductors of various size, shape, andinductance were purchased. The rated inductance of each coil used was6.8 mH (PCH-45X-685_LT, Coilcraft, Inc., Cary, Ill.), 15 mH(PCH-27X-756_LT, Coilcraft, Inc., Cary, Ill.), 68 mH (DN4546-ND,Digi-Key Corporation, Thief River Falls, Minn.), 100 mH (PCH-45X-107_LT,Coilcraft, Inc., Cary, Ill.), 220 mH (M8397-ND, Digi-Key Corporation,Thief River Falls, Minn.), and 470 mH (M8397-ND, Digi-Key Corporation,Thief River Falls, Minn.). Prior to modeling the components, theinductance and impedance of each coil were measured using a digitalmultimeter (Beckman Industrial, Fullerton, Calif.), and the overalldimensions were measured with digital calipers (Mitutoyo, Aurora, Ill.).

A comparison of these values along with the associated errors can beseen in FIGS. 8A-8B. The average errors in inductance and impedancebetween the physical inductor and the FEM were 0.30% and 0.54%,respectively. Therefore, the models accurately represent the physicalinductors under normal operating conditions.

Then, a 3D model of each coil was generated separately in COMSOL®, usingthe multi-turn coil domain feature and the parameters listed in thefollowing Table 2 such that the measured parameters corresponded to thevalues within the model.

TABLE 2 Design parameters used to build each inductor within the FEMInductor (mH) 6.8 15 68 100 220 470 Number of 407 875 1320 1591 28154110 Turns Wire Radius 0.095 0.0365 0.059 0.053 0.0352 0.0352 (mm) DCVoltage 1.62 3.89 2.92 5.91 10 10 (VDC) AC Source 0.068 0.15 0.15 0.150.50 0.50 Voltage (V_(rms)) AC Coil 22.3 17.9 68.2 71.4 100 117 Voltage(V_(pk)) Capacitance 3.14 1.416 0.321 0.222 0.1056 0.0477 (μF) Frequency1.101 1.103 1.080 1.080 1.035 1.073 (kHz)

The geometry of the six inductors was built within COMSOL® so that theycould be analyzed under both DC and AC conditions for magnetic fieldgeneration. Once the correct geometry was established for each coil,each geometry was implemented into a separate stationary FEM to evaluatethe magnetic field potential in space when used as a compensator. Inorder to accurately represent how the coils would be physically testedin the stationary domain, modulation coils as well as the TDG rod werealso modeled into the system due to the material properties and inherentmutual inductance between the modulator and compensator. This is desiredbecause the signal has to be modulated in the physical system in orderto take comparative measurements in rotation. However, it should benoted that the modulation coils were not active in this simulation asonly the DC component was being measured. The modulation coils were onlyused to represent the surrounding materials within the test fixture.Three 100 mH inductors were selected to be used for modulation and theywere oriented annularly, along with the compensator coil, around a TDGrod (13.5 mm long by 5.4 mm in diameter, MR32, Xi'an AofaOptoelectronics Technology, Inc., Xi'an, China) at 90° intervals, basedon a previously-made, 3D-printed fixture as shown in FIG. 3.

This orientation was selected to maximize the field generation along theaxis of the TDG rod. The inclusion of these materials helps accuratelyrepresent the fixture that would be used for physical measurements,allowing for the necessary interactions to occur, such as mutualinduction between coils.

The models were then surrounded by a 100 mm (in radius) spherical airdomain with a 50 mm thick infinite element shell domain to represent theanalysis over all-space and eliminate distortion of field lines alongthe boundary layer. A 3D plot was created in COMSOL®, showing themagnetic field amplitude and the direction of the field lines ascompared to current travel through the inductor. This plot, for the 470mH coil, is shown in FIG. 9A. A second plot was created to visualize theaxial component of the magnetic field along the length of the TDG rod.This plot is shown in FIG. 9B. From these plots, it can be seen that themagnetic field direction was perpendicular to the direction of currenttravel in the coil, and the largest B-field strength was localizedwithin the magnetic core domain. Similar results were obtained from eachcoil, and the peak magnetic field was shown to occur along the middle ofthe inductor when y=0 mm. The offset in symmetry, shown in FIG. 9B, wasdue to the position of the TDG rod with respect to the coil, which wasinherent to the fixture used in the physical system. Had the TDG rodbeen centered along the inductor, the resulting B-field plots would havebeen symmetric along the y=0 mm coordinate. It should also be noted thatthere was no overall relationship between individual inductors becausethey varied in size and shape. Furthermore, the results in FIGS. 9A-9Bdemonstrate the maximum B-field from each inductor, which represents arange of driving voltages based on the rated saturation current. Theseresults can be averaged along the length of the TDG rod in order topredict the maximum compensation depth seen in polarized light withcertain known parameters.

Once the geometry was complete, the material properties provided byCOMSOL® were assigned to each domain as shown in Table 3, and themulti-turn coil domain was given the necessary parameters, such as wireconductivity, wire cross section, wire direction, and number of overallturns.

TABLE 3 Material properties input to the FEM as provided by COMSOL ®.The permeability of TDG was slightly increased compared to glass due toits magnetic properties Material Domain Air Ferrite Core Copper Wire TDGPermeability 1 2000 1 1.06 Permittivity 1 1 1 4.2  Conductivity (S/m) 00 5.96 * 10⁷ 1 * 10⁻¹⁴

The material properties of glass were assigned to the TDG rod with aslight increase to relative permeability due to the magnetic propertiesof the material. Directionality of the current was determined using abuilt-in coil current calculation feature within the solver sequence,given a defined voltage input surface. Then, the initial vectorpotential was set to zero and the driving voltage was set so as to notexceed the saturation current of the coil in steady state whileremaining below 10 VDC, which is the upper limit of the multifunctiondata acquisition device (DAQ; NI USB-6212, National Instruments, Austin,Tex.) that was used. The voltages used are listed in Table 2. Finally, acustom mesh was designed such that each component, as well as the spacesbetween, could be resolved (in order to produce an accurate solution)before the solver sequence was initiated. The results were thenevaluated to show consistent magnetic field generation and the averageaxial component along the length of the TDG rod was calculated. Thiscould then be correlated to an overall rotation in polarized light of agiven wavelength, according to Equation 3. The results were used incomparison to physical rotational measurements in order to validate themodel. This process was repeated for each coil under consideration.

Once the stationary results for each coil were established, a frequencydomain analysis was performed in order to determine the maximummodulation depth. Each coil was evaluated in a similar FEM to determinethe time-dependent magnetic field generation when used as a modulator.These models were created under the frequency domain solver sequence andcontained only the coil of interest and the TDG rod, based on theorientation used for physical measurements, as shown in FIG. 3B. Thesemodels implemented the individual coil and TDG rod geometry withoutextra modulation coils in order to reflect the orientation of thephysical fixture. This orientation did not require other coils to bemodeled for modulation because the purpose of the simulation was tomeasure the modulation from a single coil, rather than to provide a DCoffset component in the presence of modulation.

These models were also assigned with A-field gauge fixing in themagnetic field domains, which was important in order to reach a stablesolution within the frequency solver sequence. This provides anadditional variable for potential and its affiliated conservationequation. A capacitance was calculated such that signal resonance couldbe achieved at a frequency between 1.0 and 1.1 kHz when driven with asinusoidal source. Then, each model was driven with a capacitive load atits resonant frequency based on physical system measurements and thecoil values given in Table 2. The model was setup to run at the selectedfrequency with a maximum AC voltage across the coil of a magnitude thatwould prevent current saturation. The results were then used tocalculate the modulation depth along the length of the TDG rod, and theoverall power consumption was determined. The steady state results aredisplayed in FIGS. 10A-10B.

The results from the 470 mH inductor are shown in a 3D color map plot inFIG. 10A. FIG. 10B shows a 2D plot of the average axial magnetic fieldcomponent along the length of the TDG rod with respect to the phaseangle of the driving source. The plot in FIG. 10B displays the maximumresults from each coil. Again, it can be seen that the magnetic fielddirection is perpendicular to the current travel, and the fieldintensity follows a sinusoidal path dependent on the frequency of thevoltage source. These results show no overall relationship betweenindividual inductors due to the same reasons described for thecompensator models. However, the peak results can be used to predict themaximum modulation depth seen in polarized light, given certain knownparameters.

Once the compensation and modulation depths of each coil wereestablished, they were compared to physical measurements in order tovalidate the accuracy of the FEM. Finally, once a model was developedfor each coil in compensation and modulation, a parametric sweep was runon each model in order to obtain a relationship between magnetic fieldstrength and driving voltage. Each model was tested over a linearvoltage range below the maximum rated value in both compensation andmodulation. The results from each coil in compensation and modulationare shown in FIG. 11A and FIG. 11B, respectively. These results indicatethat the different size, shape, and inductance of each coil provide aunique operational range of rotations based on the maximum voltage.

It should also be noted that, in certain embodiment, the 15 mH coilshould not be used in such Faraday-based polarimetric applicationsbecause of the variation in sign of the magnetic field along the lengthof the TDG rod. Due to the short length of the coil, a portion of themagnetic field along the length of the TDG rod was negative, meaningthat it will work against itself to achieve a collective rotation in onedirection. However, the magnetic field results from each coil wereaveraged and used to calculate Faraday rotation based on the drivingvoltage. The plots which relate rotation to driving voltage can be seenin FIGS. 12A-12B. These results demonstrate a linear relationshipbetween rotation and voltage in both compensation and modulation withinthe operational range of each inductor. Plots such as these are usefulfor selecting the necessary driving voltage in order to achieve arequired rotational depth in polarimetric systems with specificinductors. Given that the lines pass directly through zero, the slopecan be used for making these predictions.

The voltage sweep results were utilized to provide a comparison inmagnetic field strength between each inductor when driven with a commonvoltage source, as depicted in FIGS. 13A-13B. The 1 VDC results werecompared between coils in compensation and the 10 V_(pk) results werecompared between the coils in modulation. These results indicate thatthere was an inverse relationship between inductance and field strength.The exception to this rule is shown to be the 15 mH coil. Withoutwishing to be bound by theory, this exception is likely due to thesmaller size as compared to the other five coils. Generally, coils witha higher inductance are manufactured with more turns of wire, producinglarger resistances, and reducing the amount of current that can flowthrough the inductor. Although these coils have more turns, which alsoaffect the total magnetic field generated, the larger resistance is thelimiting factor. Therefore, in order to produce larger Faradayrotations, coils with lower inductances should be used. Then, the linearrelationship between rotation and voltage can be used to pinpoint theexact rotation needed in a given application.

After the FEM was used to predict rotational measurements, each coil wasphysically tested to measure modulation depth in a standard polarimeteras depicted schematically in FIG. 14. The test system utilized a 5 mW,543.5 nm HeNe laser (CVI Melles Griot, Albuquerque, N. Mex.) as thelight source 70, which passed through a linear polarizer (Newport,Irvine, Calif.) 80 with a vertically oriented polarization plane. Thepolarized signal proceeded through a 1.35 cm-long TDG rod (MR32, Xi'anAofa Optoelectronics Technology, Inc., Xi'an, China) before travelingthrough the analyzer 100, consisting of a second linear polarizer(Newport, Irvine, Calif.) with a horizontally oriented polarizationplane. The analyzer 100 was mounted to a rotational stage controlledthrough a DC servo motor controller (Thorlabs, Newton, N.J.) 190attached to a PC (Dell, Round Rock, Tex.) 150 running the manufacturer'sservo control software. The final signal was detected with a high speedSi photodetector (Thorlabs, Newton, N.J.) 110 and amplified with a widebandwidth amplifier (CVI Melles Griot, Albuquerque, N. Mex.) 120. Theinductor was oriented parallel to the TDG rod, matching the orientationused in the FEM. Prior to testing the coil, a series capacitance waschosen using off-the-shelf Mylar capacitors to achieve resonance at afrequency between 1.0 and 1.1 kHz.

Once the circuit was assembled, it was driven with the sinusoidalreference output of a lock-in amplifier (Stanford Research Systems,Sunnyvale, Calif.) at resonance and a maximum permitted inductor voltagebased on the saturation current of the coil through a custom poweramplifier (Marchand Electronics Inc., Rochester, N.Y.) with a gain of 40V/V. The detected signal was observed visually on an oscilloscope(Agilent, Santa Clara, Calif.), and input back to the lock-in amplifier.

Once the inductive circuit was energized, the analyzer was rotated suchthat the 2ω_(m) component was dominant and the lock-in output was zero.Then, the angular position of the analyzer was recorded, the stage wasrotated until the 2ω_(m) signal was eliminated, and the final angularposition was recorded. The change in rotation represents the totalmodulation depth for a given inductor, driving voltage, and orientationwhen the polarizer and analyzer were initially crossed, and the detectedoutput was centered around zero. The 2ω_(m) signal was completelyeliminated when the analyzer had rotated just enough so that the peak ofthe modulated signal no longer crossed the null plane of the analyzer,and the detected signal was of the same frequency as the referencesignal (ω_(m)). This process was carried out in triplicate and averagedfor each coil before comparing values to the FEM output. The averagedresults of measured rotation versus the FEM-calculated rotation wereplotted in MATLAB, as shown in the right side of FIG. 16.

The standard deviation of the residuals of the rotational data based onthese measurements was then calculated to determine a prediction errorbetween measurements and the FEM calculations. The error in predictionof modulation was calculated to be 0.0044°, which is 0.71% of thelargest rotation seen in the data. Therefore, the developed FEM canaccurately predict the depth of Faraday modulation for variousoff-the-shelf inductors.

After the modulation depth of each coil was measured, a similar processwas used for measurement of the maximum compensation depth that eachcoil was capable of achieving with the addition of a modulationcomponent to be used for signal detection, when driven with a DC voltagesource. Modulation was necessary due to the sensitivity required formeasuring millidegree polarization rotations. The same polarimetersystem described above was used with the addition of the modulationcomponent, which consisted of three 100 mH coils, surrounding the TDGrod as shown in FIG. 3A, and a 0.0823 μF series capacitance. Once thesystem was assembled into the test fixture, the modulator was drivenwith a 20 V_(rms) sinusoidal signal at a frequency of 1.1 kHz, and theanalyzer was rotated until the lock-in output was zero. Then, theangular position was recorded, and the compensator was powered with a DCpower supply (Hewlett-Packard Company, Palo Alto, Calif.) with the sameinductor voltage used in the equivalent FEM so as to avoid currentsaturation and avoid exceeding the 10 VDC limit of the DAQ. The analyzerwas rotated again until the lock-in output was zero and the 2ω_(m)signal was dominant before recording the final angular position. Thetotal rotation represents how far from the null plane that thecompensator coil caused the signal to rotate based on the Faradayeffect. This process was also carried out in triplicate and averaged foreach coil before comparing values to the equivalent FEM output.

The results of measured rotation versus the FEM-calculated rotation wasplotted in MATLAB, as shown in the left side of FIG. 16. Based on theseresults, the error in prediction of compensation was calculate to be0.0087°, which is 3.26% of the largest rotation seen in the data series.Although this was higher than the modulator prediction error, it wasstill within reasonable accuracy for successful compensator predictionand coil selection. Without wishing to be bound by theory, it isbelieved the primary source of this error was due to the difficulty ofmeasuring angles with sub-millidegree sensitivity, rather than generaldiscrepancies within the FEM. Using a mechanical rotational stage formeasuring polarization angles of this magnitude was reasonable but stillproduces inherent error. Also, the placement of the coil with respect tothe TDG rod largely affects the rotational results, meaning that anyslight difference between the fixture and the FEM geometry could alsoproduce error. However, it was demonstrated that the overall modelprovides an accurate representation of the physical system.

Example 2 Optimization of the IFMC System to Predict PhysiologicalGlucose Concentrations

The results above demonstrate that the FEM successfully predicts Faradayrotation in both compensation and modulation components in apolarimetric system. Because a commercial noninvasive glucose sensorwould benefit the diabetic community by offering an accurate alternativeto the current invasive means of detection, saving costs in health, andimproving overall patient health and compliance, the IFMC system wasconfigured for use in the noninvasive polarimetric sensing of glucose.The primary size and cost factor in these systems has been theseparation of Faraday modulation and compensation components, which asdiscussed above previously needed multiple optical rods and custom-builtinductive coils.

A typical physiological glucose detection system may have to sense bloodglucose concentrations as high as 600 mg/dL under hyperglycemicconditions. Given the specific rotation of D-glucose, apolarimetric-based system would need to be able to resolve a range ofrotation between 0 and 63.2 millidegrees, given a 1 cm path length(characteristic of the aqueous humor of the eye, where noninvasivesensing is likely to take place), a source wavelength of 543.5 nm, and aworst-case concentration of 1000 mg/dL. Therefore, an effective Faradaycompensator component should obtain a rotation of at least 0.0632° so asto fully encompass this range. Similarly, an effective Faraday modulatorshould obtain a modulation depth of at least 1°, which is much largerthan the maximum rotation that may occur due to glucose.

To design the IFMC system, the maximum FEM data from Example 1 wasplotted in MATLAB, as shown in FIG. 17. These plots were used to selectthe optimal coils for device design. The plots represent compensationdepth versus driving voltage (left) as well as modulation depth versusaverage power consumption (right). These types of plots are useful forselecting a compensator coil to be used in an IFMC system when a minimumrotation is needed and there is a maximum voltage allotted by thedriving electronics. The minimum rotational requirement for aphysiological glucose sensor is presented as the blue horizontal line onthe plot on the left of FIG. 17. These plots are also useful forselecting a modulator configuration to be used in an IFMC system when aminimum depth must be achieved while maintaining low power. Points onthe upper-left side of the plot on the right of FIG. 17 represent thehighest rotation-to-power ratio (RTPR).

The coil selected to operate as the compensator was the 220 mH inductorbecause it was able to achieve a rotation of 0.0740°, which is largerthan the minimum requirement of 0.0632° and it can utilize the full 10VDC range of the DAQ used in feedback control. Due to the fact that nosingle coil was able to achieve a modulation depth larger than 1°, three100 mH coils connected in series were selected to operate as themodulator component. These coils were selected because they produce anindividual modulation depth of 0.4881° and have the highest RTPR of0.99619 W. Once the coils were selected, a FEM was built to reflect theproperties of the coils, surrounding the parallel TDG rod. Initially, astationary analysis was computed with a 10 VDC source applied to the 220mH coil in order to predict the maximum possible compensation depth.Then, a frequency domain analysis was computed with a 45 V_(rms)sinusoidal source at a frequency of 1.073 kHz applied to each 100 mHcoil. These resulted in a total compensation depth of 0.0780° andmodulation depth of 1.2404°, indicating that both requirements weresuccessfully met by the IFMC system. The average power calculated forthe modulation circuit was 1.99 W, which produces a RTPR of 0.6233°/W.The decrease in this figure when compared to individual 100 mH coils wasdue to the mutual induction losses between coils, which also explainswhy the total modulation depth was not simply three times as large asthe depth produced by a single coil. A 3D color map plot of the IFMCsystem in compensation and modulation from COMSOL® is shown in FIGS.18A-18B. Both images indicate the expected interaction between coilcurrents and magnetic field, which further supports the FEM.

The DC axial component of the magnetic field was averaged along thelength of the TDG rod and the corresponding rotation was calculated.Next, the total inductance and impedance was measured and a capacitancewas calculated such that signal resonance would occur at a frequencybetween 1 and 1.1 kHz when drive with a sinusoidal voltage source basedon Equation 16:

$\begin{matrix}{{2\pi \; f} = \frac{1}{\sqrt{LC}}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

where f is the frequency, L is the inductance, and C is the capacitance.The calculated capacitance was also attached in series with themodulator coils. Circuit analysis was conducted to determine the voltagedrop across each coil when driven with a 20 V_(rms) signal at resonance.Finally, these parameters were assigned to the modulator coils withinthe FEM such that current would travel in the same direction around eachcoil, and the frequency domain study was computed. The results were usedto determine the AC axial component of the magnetic field along thelength of the TDG rod, and the corresponding modulation depth wascalculated.

Once the FEM indicated that the IFMC system meets the designrequirements, a physical IFMC system was produced using three seriallyconnected 100 mH inductors as the modulator and one 220 mH inductor asthe compensator. The four coils were assembled to replicate the FEM, andfixed in a custom, hand-held housing that was designed in SolidWorks®system (SolidWorks Corporation, Waltham, Mass.) and fabricated with a 3Dprinter (Objet, Rehovot, Israel) as shown in FIG. 3.

Within the housing, the coils were oriented parallel and annularly at90° intervals around a TDG rod (13.5 mm long by 5.4 mm in diameter). Thethree modulator coils were connected in series such that current wouldflow in the same direction around each coil, producing a collectivelymaximized axial component of the magnetic field along the TDG rod whichis important for effective Faraday modulation. All electricalconnections were soldered together. The terminals for the compensatorand modulator were attached to a 6-pin mini circular connector(illustrated in FIG. 3 as 52), and mounted to the external surface ofthe housing. Standard 30 mm optical cage mounts and ¼-20 threaded postmounts were used for easy integration with standard optical equipment.Also, the interior was designed such that different inserts would allowfor a variety of off-the-shelf inductors to be used at various distancesfrom the centered TDG rod, providing a universal kit for a wide range ofdifferent polarimetric applications. The final design was thenintegrated with the polarimetric system used for rotationalmeasurements, and the total compensation and modulation depths weredetermined.

After the final assembly was coupled to the polarimetric system, it wastested to measure modulation and compensation depth. Once the system wasfully assembled, the modulator produced a measured inductance of 245 mHand an impedance of 201Ω. Therefore, a total capacitance measuring0.0898 μF was serially connected to the modulator coils in order toachieve signal resonance at a frequency of 1.073 kHz when driven with asinusoidal voltage source. The final assembly produced a modulationdepth of 1.2226° when driven with a 20 V_(rms) sine wave at 1.073 kHz,producing a measurement error of 1.44%. The compensator coil produced ameasured inductance of 227 mH, an impedance of 358Ω, and an averagerotation of 0.0794° when excited with a 10 VDC source, producing ameasurement error of 1.70%. Therefore, the IFMC system is capable ofmeeting the minimum requirements of 0.0632° in compensation and 1° inmodulation for successful physiological glucose detection. Furthermore,the overall error associated with the IFMC system demonstrates that aFEM can be used to successfully design and optimize the componentswithin a specific polarimetric application.

Example 3 Validation of an IFMC System

The IFMC system was validated under two separate conditions. First,static measurements were taken to formulate a calibration model andcalculate errors in prediction. Second, a dynamic flow system wasdesigned to control glucose concentrations in real time so thatmeasurements could be taken continuously. Accordingly, the IFMC systemwas tested in a polarimetric system against glucose-doped water in astatic sample cell and a dynamic flow system programmed with aphysiological glucose profile.

The IFMC system of Example 2 was validated using a single wavelengthdigital closed-loop polarimeter. The system utilized a 5 mW, 543.5 nmHeNe laser (CVI Melles Griot, Albuquerque, N. Mex.) as the light source,which passed through a linear polarizer (Newport, Irvine, Calif.) with avertically oriented polarization plane. The polarized signal thenproceeded through a custom sample cell with a 1 cm path length beforetraveling through the IFMC system. Finally, the modulated signal waspassed through an analyzer consisting of a second linear polarizer(Newport, Irvine, Calif.) with a horizontally oriented polarizationplane, before being detected with a high speed Si photodetector(Thorlabs, Newton, N.J.) and amplified with a wide bandwidth amplifier(CVI Melles Griot, Albuquerque, N. Mex.). The modulator was driven withthe sinusoidal reference output of a lock-in amplifier (StanfordResearch Systems, Sunnyvale, Calif.) at a voltage of 0.5 V_(rms) and afrequency necessary for achieving signal resonance through a custompower amplifier with a gain of 40 V/V (Marchand Electronics Inc.,Rochester, N.Y.). The detected signal was input to the lock-in amplifierand observed visually on an oscilloscope (Agilent, Santa Clara, Calif.).The output from the lock-in amplifier was captured by a multifunctiondata acquisition device (DAQ, National Instruments, Austin, Tex.) andread on a PC (Dell, Round Rock, Tex.). The information was processed ina PID continuous feedback VI created in Lab VIEW (National Instruments,Austin, Tex.). The feedback loop controlled a voltage buffer circuitpowered with a DC power supply (Hewlett-Packard Company, Palo Alto,Calif.) through the DAQ which would apply a DC voltage to thecompensator coil in order to align the polarized signal perpendicularlyto the analyzer by magnetic field generation, centering the modulatedsignal on the null plane, and producing a detected signal with afrequency of twice the reference signal. This applied voltage wasproportional to any rotation in the polarized signal that would occurwithin the system, such as that due to glucose within the sample cell.Therefore, the output from the PID controller could be directly used topredict the glucose concentration in unknown samples of fixed pathlength with a linear calibration model.

Static Glucose Detection

In order to compare the IFMC system to other Faraday-based glucosedetection systems, polarimetric measurements were taken in thehypoglycemic and hyperglycemic concentration ranges. Static validationof the IFMC system was carried out using a polarimetric system asdepicted schematically in FIG. 15, with a 1 cm open-air sample cell 290that allowed for liquid to be easily pipette into and out of the lightpath, contained between two glass microscope cover slides (Thermo FisherScientific, Waltham, Mass.). The modulated signal was monitored with thelock-in amplifier 230 which output a signal to the DAQ (NI USB-6212,National Instruments, Austin, Tex.) 240 and onto a PC 250. Theinformation was processed in a PID continuous feedback virtualinstrument (VI) created in LabVIEW (National Instruments, Austin, Tex.).The feedback loop controlled a voltage buffer circuit (LT1010, LinearTechnology, Milpitas, Calif.) 260 powered with a DC power supply(Hewlett-Packard Company, Palo Alto, Calif.) 280 through the DAQ 240which would apply a DC voltage to the compensator coil 24 in order toalign the polarized signal perpendicularly to the analyzer by magneticfield generation, centering the modulated signal on the null plane andproducing a 2ω_(m) detected signal. This applied voltage wasproportional to any rotation in the polarized signal that would occurwithin the system, such as that due to glucose within the sample cell.Therefore, the output from the PID controller could be directly used topredict the glucose concentration in unknown samples of fixed pathlength with a linear calibration model over a known range.

To begin, glucose solutions were prepared in 2 mL volumes usingdeionized (DI) water and a 1000 mg/dL glucose stock. The stock solutionwas created with a powder form of D-(+)-glucose (Sigma-Aldrich, St.Louis, Mo.) 24 hours prior to polarimetric testing in order to achievecomplete mutarotation equilibrium. Standard dilutions were made in thehypoglycemic range from 0 to 100 mg/dL in intervals of 10 mg/dL as wellas in the hyperglycemic range from 0 to 600 mg/dL in intervals of 50mg/dL. The solutions were pipetted at random into the sample cell foreach dilution range and the compensator voltage was noted. The samplecell was rinsed with DI water between measurements.

Two separate data sets were collected for both concentration ranges.Calibration models were formulated using least-squares linear regressionfor each concentration range after subtracting the baseline measurement.Then, the data was plotted and the errors of calibration and predictionwere calculated in MATLAB (MathWorks, Natick, Mass.). The standard errorof calibration (SEC) was calculated by evaluating the calibration dataset and determining the standard deviation of the residuals against theexpected values, as shown in Equation 17:

$\begin{matrix}{{SEC} = \sqrt{\frac{1}{\left( {N - 1} \right)}{\sum\limits_{i = 1}^{N}\; \left( {C_{i} - \overset{\_}{C}} \right)^{2}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

where C is the set of residuals from the calibration data.

The standard error of prediction (SEP) was calculated in a similarfashion but by evaluating a separate data set, not used in calibration,according the following Equation 18:

$\begin{matrix}{{SEP} = \sqrt{\frac{1}{\left( {N - 1} \right)}{\sum\limits_{i = 1}^{N}\; \left( {P_{i} - \overset{\_}{P}} \right)^{2}}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

where P is the set of residuals from the prediction data. The residualsare the difference between the predicted and actual concentration.

The calibration and prediction results for the hypoglycemic andhyperglycemic concentration ranges against the actual concentrationvalues are shown by FIGS. 19A-19D, where the calibration results forhypoglycemic concentrations and hyperglycemic concentrations are shownin FIGS. 19A-19B, respectively, and the prediction results forhypoglycemic concentrations and hyperglycemic concentrations are shownin FIGS. 19C-19D, respectively. The hypoglycemic data resulted in a SECof 1.6 mg/dL with an R² of 0.9977 and a SEP of 1.8 mg/dL with an R² of0.9970. The hyperglycemic data resulted in a SEC of 5.2 mg/dL with an R²of 0.9993 and a SEP of 5.4 mg/dL with an R² of 0.9992. The main sourceof error within the system was due to the sensitivity required tomeasure sub-millidegree rotations. Although optical systems are capableof accurately detecting these measurements, electromagnetic noise andphysical vibrations play a noticeable role in the overall capabilitiesof these systems. These results show that the IFMC system is capable ofachieving measurement sensitivity with similar, if not better, accuracythan the larger, two-part modulator/compensator devices.

Flow System Validation

A flow system reproduces the physiological conditions experienced inanimal models without the need for actual animal testing. A primarytesting characteristic of in vivo systems is the capability to trackphysiological glucose profiles in real-time. A programmable glucose flowsystem capable of being integrated with the polarimeter PID controlprogram was thus developed, providing real-time output as it correspondsto changing glucose concentrations. The programmable flow system wascomposed of four WPX1 peristaltic pumps with stepper motors (WELCO Co.,Ltd., Tokyo, Japan) and all-purpose silicon Tygon tubing (Saint-GobainS.A., Courbevoie, France). A schematic of the flow system coupled to thepolarimeter is shown in FIG. 20.

Pump 1 (WPX1-S3/16FA4-W4C-CP) was set up to run continuously tocirculate glucose solutions from a well-mixed central flask, through acustom-designed and 3D-printed 1 cm flow cell that was sealed on eitherside with glass microscope cover slides, and back into the central flaskfor continuous mixing. One example of a custom-designed flow cell isshown in FIG. 21. Pump 2 (WPX1-S1/8FB4-W4C-YP) would remove waste fromthe central flask to maintain a constant liquid volume duringconcentration changes. Pump 3 (WPX1-S3/32FB4-WM4-BP) would add DI waterto the central flask during a concentration decrease. Pump 4(WPX1-S3/32FB4-WM4-GP) would add a 1000 mg/dL glucose stock solution tothe central flask during a concentration increase.

The stepper motors on each pump were driven with a Quadstepper MotorDriver Board (SparkFun Electronics, Boulder, Colo.), which wascontrolled through an Arduino Mega 2560 R3 Microcontroller Board(Officine Arduino Torino, Torino, Italy). The microcontroller wasprogrammed with a customized version of the open source LabVIEWInterface for Arduino toolkit (LIFA) through the Arduino developmentsoftware which was capable of running the Quadstepper Motor DriverBoard. Both the Arduino programming environment and the LIFA toolkitwere downloaded as open source applications from the internet.

Three separate LabVIEW VIs were developed and integrated to thepolarimeter PID VI for collecting real-time glucose measurement databased on the polarimeter response as related to actual concentration inthe flow cell. The first VI was used to purge the tubing prior to eachexperiment in order to fill the lines with the corresponding solutionsand remove air bubbles. The second VI was designed for changing glucoseconcentrations as the system was running for calibration and testingpurposes. The third VI was used for programming predefined glucoseprofiles to run continuously over a designated period of time in orderto mimic the physiological interactions between insulin and glucose.Each VI was designed with the appropriate fields for updating real-timeconcentration, monitoring or changing the stepper motor status, trackingflask concentration and volume, and visualizing the polarimetric output.

When the flow system was running, the central flask was maintained at aconsistent 50 mL volume and continuously mixed on a magnetic stir plate(Corning, Tewksbury, Mass.). When the concentration was changed in thecentral flask, the waste pump would pull out the allotted volume ofliquid prior to the addition of glucose stock or water in order tominimize equilibrium time. Also, the circulation pump utilized a minimallength of tubing, set to run at a flow rate of 51.187 mL/min. Allconcentration changes were spaced at two-minute intervals in order toallow adequate time for system equilibrium. Prior to initial use, eachpump was calibrated using DI water and an analytical balance by weighinga sample dispensed from 10 rotations of the pump head and calculating avolume per rotation figure. This would allow for maximum accuracy overlong periods of time when programmed into the flow system VI. It wasdetermined that pumps 1, 2, 3, and 4 would dispense 0.910, 0.472, 0.337,and 0.336 mL per revolution of the pump head, respectively. These valueswere programmed into the flow system VI and standard glucose dilutionsin the hypoglycemic and hyperglycemic range were created.

The system was then validated by mixing glucose solutions of knownconcentration using the flow system. The glucose concentration in thecentral flask was ramped up from 0 to 100 mg/dL in 10 mg/dL intervalsand again from 0 to 600 mg/dL in 50 mg/dL intervals. After theconcentration equilibrated with each change, 2 mL samples were removedand the flask volume within the LabVIEW VI was adjusted accordingly forcorrect concentration calculations. The samples were then compared tomeasurements taken with a YSI 2300 STAT Plus Glucose and LactateAnalyzer (YSI Life Sciences, Inc., Yellow Springs, Ohio) in triplicate,and the system error was calculated. The averaged data resulted in astandard error of 0.5 mg/dL in the hypoglycemic range and 6.4 mg/dL inthe hyperglycemic range. These values were within the limits of the YSI,per the manufacturer's documentation. Given the precision control of thestepper motor-driven pump heads and the individual calibration of eachhead, the primary source of error was likely centered on the YSI rat herthan the flow system. The flow system was proven to be capable ofproducing accurately-controlled real-time glucose solutions in order tofacilitate robust continuous polarimetric measurements similar tostandard in vivo experiments.

Continuous Dynamic Glucose Detection

Once the flow system was validated, the IFMC system was evaluated in areal-time dynamic system using the glucose flow system and a custom 1 cmflow cell. A different calibration model was created for the polarimeterwith the custom flow cell and the IFMC system. This was done byaveraging three collected data sets, less the baseline measurements,over a range of 0 to 200 mg/dL, and fitting the data to a least-squareslinear regression model. This calibration model resulted in a SEC of 3.5mg/dL with an R² of 0.9972, which is in similar agreement with thestatic glucose data.

Prior to running the 500-minute physiological glucose profile with theIFMC system, a new calibration model was formulated for the flow cell.This was done by averaging three collected data sets, less the baselinemeasurements, over a range of 0 to 200 mg/dL, and fitting the data to aleast-squares linear regression model. 50 mL glucose solutions were madein DI water between 0 and 200 mg/dL in 20 mg/dL intervals. Each solutionwas purged through the flow cell at random while running the PID VI, andthe voltage output to the polarimeter was noted. The flow cell wasflushed with DI water between each measurement, and the baseline voltagewas noted. This process was carried out in triplicate, and the baselinewas subtracted from each data point. The data sets were averaged, and afinal least-squares linear regression calibration model was formed. Thenew calibration model resulted in a SEC of 3.5 mg/dL with an R² of0.9972, which is in similar agreement with the static glucose data. Thismodel was then programmed into the PID VI so that continuous glucosemeasurements could be taken and monitored through the flow system VI totrack a physiological concentration profile over time.

The glucose profile used for continuous monitoring was calculated with amathematical model that simulates the human ultradian oscillations ofinsulin and glucose. The six-state differential system was solved usingXPPAUT, an open source numerical integration software package. The finalprofile reflects the glucose response in a non-diabetic person followinga 50 g oral glucose tolerance test (OGTT) beginning with fasting glucoseand insulin levels using the gastrointestinal absorption rate equationas the glucose input parameter. The profile data was exported to MATLABand saved as a two-column text file containing time in two-minuteintervals for a duration of 500 minutes (beginning with t=2 min) and thecorresponding glucose concentrations in mg/dL. The data was thenuploaded into the flow system profile VI which would update the glucoseconcentration in the central flask every two minutes, producing acontinuous physiological profile for the polarimeter to monitor throughthe flow cell.

Prior to beginning the 500-minute continuous glucose monitor experiment,50 mL of DI water was added to the central flask and purged through theflow cell so that no air bubbles remained in the circulation path. Withthe circulation pump and stir plate running, the polarimeter was turnedon and the initial baseline measurement was set in the calibration modelwithin the PID VI. Then, the concentration in the central flask wasbrought to an initial 80 mg/dL and the flow system profile VI wasstarted at t=0 min. The polarimeter output was plotted in real-time at afrequency of 1 Hz along with the actual concentration in the centralflask. After the 500-minute testing period, the system was shut down andthe final data set containing the polarimeter output was exported andsaved. The data was then imported into MATLAB where it was plotted andthe errors for continuous measurements over time were calculated. Thesame continuous test was repeated two more times for a total of threedata sets.

The raw data results of the continuous polarimeter output are shown inFIG. 22, as compared to the actual real-time glucose concentration inthe central flask. As shown in FIG. 22, the polarimeter tracked theoverall profile with precision. However, as time went on, the outputsignal drifted with respect to the actual profile. In order to quantifythe error over time, the SEP was calculated at 100-minute intervalsusing the raw data. The SEPs during the first 100, 200, 300, 400, and500 minutes were determined to be 4.3, 3.7, 3.2, 3.1, and 3.2 mg/dL,respectively. Based on these results, the system is capable of trackingconcentration changes with a precision that is consistent with thecalibration model. The calibration model remains valid, but the baselineshifted. In order to quantify the baseline drift, the mean of theresiduals was also calculated over the same 100-minute intervals to be4.2, 5.3, 5.2, 5.7, and 6.2 mg/dL, respectively. These results show aconsistent decrease in system accuracy as drift occurs over time. Thecause for the drift is explained due to the physical sensitivity of thesystem. Although the optical components were mounted on an optical tableand supported with 30 mm cage mounts, the slightest table movement canlead to spikes in the system output (as shown around the 210-minute markin FIG. 22). This coupled with consistent vibration of the drivingelectronics, the stir plate, and the peristaltic pumps on the table cancause the position of each component in the system to slightly shiftover time, resulting in a change in the polarization state of thesignal. Furthermore, the branching off of the data during the last 20minutes of the experiment was caused by an air bubble that becametrapped in the flow cell. Air bubbles can be minimized or eliminated byalternate designs for the interior volume of the flow cell.

A final analysis on the data was conducted to realign the baseline every20 minutes to the calibration model before running a 60-second movingaverage. This type of baseline correction can be rationalized due to thenature of the final system that is to be used by diabetics. Continuousmeasurements are preferred for achieving accurate results. However, ahand-held glucose meter would be used by patients on the order of a fewminutes, meaning that baseline measurements can be taken before andafter each reading. Applications that require long-term monitoring, suchas use with sugar monitoring in cell culture bioreactors, can bedesigned to implement single-point baseline corrections, which arecommon for many commercial glucose meters such as the YSI.

The baseline-corrected results, shown in FIG. 23, demonstrate a muchbetter fit to the actual concentration profile. It should be noted thatthe system was not recalibrated as the model was still valid based onthe SEP, but rather the baseline was shifted accordingly and theexcessive noise was masked. The branching off of the data in the last 20minutes of the experiment was caused by an air bubble that becametrapped in the flow cell. Problems such as these could be minimized byredesigning the interior volume of the flow cell. Air bubbles areprimarily an issue with sample cell design, and therefore would not be aproblem during actual physiological sensing. The final baselinecorrected SEP was calculated to be 3.5 mg/dL with the overall mean ofthe residuals to be 0.2 mg/dL. These results indicate that thebaseline-corrected data maintains similar error to the calibration modelas well as to the raw data while the drift is negated.

The real-time test was repeated two more times, and the results areshown in FIGS. 24-25. Both of these plots display various baseline driftover time due to vibrational effects, similar to the initial results,further indicating the overall sensitivity of the polarimetric system.The second trial resulted in an overall SEP of 7.9 mg/dL from the rawdata, and a SEP of 4.2 mg/dL after performing the same baselinecorrection and moving average. The third trial resulted in an overallSEP of 10.3 mg/dL from the raw data, and a SEP of 3.6 mg/dL afterbaseline correction. Therefore, the results are repeatable and asingle-point baseline correction can be used to realign any vibrationalbaseline drift.

After determining the IFMC system can successfully track a non-diabeticphysiological glucose profile over time based on a controllablemathematical model, the test was repeated with two different profiles.First, the system was tested against a clinical profile from a patientwith type 1 diabetes, providing information following meal ingestion andinsulin injections. Then, the limitations of the flow system and IFMCsystem were tested against a near-step change profile with a maximumrate of change in concentration of 27.5 mg/dL/min and an average changeof 10 mg/dL/min. The results from these additional experiments aredisplayed in FIGS. 26-27, respectively.

The diabetic profile resulted in an overall SEP of 4.8 mg/dL, with abaseline-corrected SEP of 3.4 mg/dL. The near-step profile resulted inan overall SEP of 11.1 mg/dL, with a baseline-corrected SEP of 5.4mg/dL. The diabetic profile demonstrated good tracking, even in the rawdata, while the step profile showed a variable amount of baseline drift.The SEP encountered from the raw data is variable, depending on theoverall amount of drift. However, the single-point baseline correcteddata provides a better representation of the system, with an average SEPof 3.8 mg/dL from all data sets. This indicates that the relative amountof drift that occurs in the system is situational, and the single-pointbaseline correction can successfully combat this issue. Furthermore,these results demonstrate that the IFMC system can successfully track aclinical diabetic profile during normal conditions as well as during theworst-case conditions, which are represented by the high rate of changeseen in the near-step change profile. Regardless of the drift, theresults show that the IFMC system is capable of achieving the necessaryrotational sensitivity and stability required for continuousphysiological glucose detection.

Overall, these results demonstrate that the IFMC system can performsimilar to, if not better than, the larger two-partmodulator/compensators. The IFMC system is thus a useful component fornoninvasive polarimetric glucose detectors. This device is beneficial inpersonalized glucose monitors for diabetic patients because itconsolidates size and cost requirements and can achieve the same effectas its two-part predecessors. The examples show not only that the IFMCsystem meets the minimum design requirements for physiologicaldetection, but also that it maintains a degree of sensitivity similarto, if not better than, previously tested configurations with overallSEPs of 1.8 mg/dL and 5.4 mg/dL in the hypoglycemic and hyperglycemicconcentration ranges, respectively.

Certain embodiments of the devices and methods disclosed herein aredefined in the above examples. It should be understood that theseexamples, while indicating particular embodiments of the invention, aregiven by way of illustration only. From the above discussion and theseexamples, one skilled in the art can ascertain the essentialcharacteristics of this disclosure, and without departing from thespirit and scope thereof, can make various changes and modifications toadapt the compositions and methods described herein to various usagesand conditions. Various changes may be made and equivalents may besubstituted for elements thereof without departing from the essentialscope of the disclosure. In addition, many modifications may be made toadapt a particular situation or material to the teachings of thedisclosure without departing from the essential scope thereof.

What is claimed is:
 1. A method of conducting integrated Faradaymodulation and Faraday compensation comprising: generating a firstmagnetic field from an AC current; generating a second magnetic fieldfrom a DC current; and superimposing the first magnetic field and thesecond magnetic field onto a single optical material.
 2. A method ofmeasuring changes in a state of polarization of a beam of light,comprising: generating a first magnetic field from an AC current;generating a second magnetic field from a DC current; and superimposingthe first magnetic field and the second magnetic field onto a singleoptical material.
 3. A method of measuring changes in a state ofpolarization in a sample, comprising: a) passing polarized light througha sample or reflected from a surface of the sample such that the stateof polarization of the light is changed; b) allowing the changedpolarized light of step a) to pass through an optical material having adesired Verdet constant; c) providing separate AC and DC magnetic fieldsources to the optical material; the AC magnetic source producing afirst magnetic field for fast polarization modulation; and, the DCmagnetic source producing a second magnetic field for polarizationfeedback compensation; d) superimposing the separate first and secondmagnetic fields within the optical material as the polarized light ofstep b) passes through the optical material of step c); e) passing thepolarized light of step d) through an analyzer; f) allowing the light ofstep e) to impinge onto a detector; g) providing a feedback signal to atleast one DC magnetic field source; h) measuring changes in a state ofpolarization in the sample; and, optionally i) adjusting at least one DCmagnetic field source based on the feedback signal of step g).
 4. Amethod of claim 3, wherein changes in the state of polarization arecalibrated, based on the feedback signal of step g), to one or more of:concentration of an analyte in the sample, layer thickness of thesample, surface characteristics of the sample, and material comprisingthe analyte and/or sample.
 5. A method of claim 3, wherein step h)includes varying ranges of modulation depths and/or varying ranges ofcompensation depths of one or more of the magnetic fields.
 6. A methodof claim 3, further including step j) controlling modulation andcompensation depth by varying one or more of parameters selected from:coil permeability, conductivity, wire radius, or number of turns, in theAC and/or DC magnetic field sources; location of the AC and/or DCmagnetic field sources with respect to each other and/or to the opticalmaterial; orientation of the AC and/or DC magnetic field sources withrespect to each other and/or to the optical material; and, current drivewithin the AC and/or DC magnetic field sources.
 7. A method of claim 3,wherein the sample is an optically active material.
 8. A method of claim7, wherein the optically active material comprises glucose.
 9. A methodof claim 8, wherein the glucose is present in aqueous humor of an eye,and the method comprises detection of glucose concentrations through theaqueous humor of the eye.
 10. A method of claim 1, wherein the samplecomprises a material having surface variations.
 11. A method of claim10, wherein the material having surface variations comprises a thin filmmaterial.
 12. A method of claim 1 wherein a component apparatus isadjustable to allow for an operational range for modulation between 0°and 2°.
 13. A method of claim 1, wherein a component apparatus isadjustable to allow for an operational range for compensation between 0°and 0.5° with sub-millidegree rotational sensitivity.
 14. A method ofclaim 1, wherein the method comprises achieving a modulation depth ofabout 1° and a maximum compensation depth of about 0.0632°.
 15. A methodof claim 1, wherein an AC power supply to the AC magnetic field sourcesustains a desired modulation depth to the magnetic fields beingsupplied to the optical material; and, wherein a DC power supply to theDC magnetic field source supplies a sub-millidegree rotationalsensitivity to the magnetic fields being supplied to the opticalmaterial.